How to get a plane to intersect and join/merge with the perpendicular plane?
You want to stick this edge to this face but this is not a clean topology because your edge will just float, you should first use the knife tool to cut the roof and the left side, in order to add vertices, then fill with faces between the vertices with some F, and at last delete the inner faces:

Edit with your current file, as we can see you have floating edges, inner faces, etc:

What should happen: